Chapter 1.1, Problem 7CP

Use the Bisection Method to find the two real numbers $x$ , within six correct decimal places, that make the determinant of the matrix

$A=\left[\begin{array}{rrrr}\hfill 1& \hfill 2& \hfill 3& \hfill x\\ \hfill 4& \hfill 5& \hfill x& \hfill 6\\ \hfill 7& \hfill x& \hfill 8& \hfill 9\\ \hfill x& \hfill 10& \hfill 11& \hfill 12\end{array}\right]$

equal to 1000. For each solution you find, test it by computing the corresponding determinant and reporting how many correct decimal places (after the decimal point) the determinant has when your solution $x$ is used. (In Section 1.2, we will call this the "backward error” associated with the approximate solution.) You may use the MATLAB command det to compute the determinants.